# Value of a Statistical Life under Large Mortality Risk Change: Theory and an Application to COVID-19

Diego S. Cardoso and Ricardo Dahis. (R&R)

Abstract In the estimation of the benefits of mortality reduction, a simple approach is to multiply the value of a statistical life (VSL) by the expected reduction in fatalities, thus holding the VSL constant. This procedure approximates benefits for small changes in mortality, but inaccurately characterizes benefits for large risk changes because it does not account for variations in the VSL. Building on the theoretical framework of the VSL, we outline a practical approach to calculate the benefits of large mortality reductions. This approach is readily applicable, yielding closed-form expressions that only require statistics broadly available for VSL-based calculations. Using recent empirical estimates of the VSL, we apply this approach to estimate the benefits of social distancing to combat COVID-19 in the United States and Brazil, two of the countries most affected by the pandemic. Our findings show that social distancing generates a benefit of \$4–4.4 trillion in the United States, and \$0.6 trillion in Brazil. We extend this analysis to other 72 countries using VSL projections and find that benefits correspond to 17% of the gross national income on average. Our results indicate that the constant VSL approach overestimates the benefits of social distancing by 74% on average.